Graph partitioningis a hlndamental problem ill really scientific settillgs. This document describes the capabilities and operation of Chaco, a software package designed to partition graphs. Chaco allows for recursive application of any of several different methods for finding small edge separators in weighted graphs. These methods include inertial, spectral, Kernighan-Lin and multilevel methods in addition to several simpler strategies. Each of these methods can be used to partition the graph into two, four or eight pieces at each level of recursion. In addition, the Kernighan-Lin method can be used to improve partitions generated by any of the other methods. Brief descriptions of these methods are provided, along with references to releva.llt literature. The user illterrace, input/output formats and appropriate settings for a variety of code parmneters are discussed in detail, and some suggestions on algorithm selection are olfered.
Photolithography systems are on pace to reach atomic scale by the mid-2020s, necessitating alternatives to continue realizing faster, more predictable, and cheaper computing performance. If the end of Moore's law is real, a research agenda is needed to assess the viability of novel semiconductor technologies and navigate the ensuing challenges.
Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. We present a new domain mapping algorithm that extends recent work in which ideas from spectral graph theory have been applied to this problem. Our generalization of spectral graph bisection involves a novel use of multiple eigenvectors to allow for division of a computation into four or eight parts at each stage of a recursive decomposition. The resulting method is suitable for scientific computations like irregular finite elements or differences performed on hypercube or mesh architecture machines. Experimental results confirm that the new method provides better decompositions arrived at more economically and robustly than with previous spectral methods. We have also improved upon the known spectral lower bound for graph bisection.
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